They got lucky and a handful of their early patents became required parts of early cellular standards. Since then they've lobbied the standards bodies to include features that require their newest patents. When that fails, because the mobile manufacturers are tired of Qualcomm's monopoly, they simply buy up more patents to make up the difference.
Yet, they recovered, and clawed back their way to the top, with only MediaTek now threatening them.
I don't expect MediaTek to be as inept, and Pavlovian if Qualcomm will ever come to them with a deal, as they did with Allwinner 8 years ago (Allwinner gave up on mobile market, and Qualcomm gave them an obscene cut from their low-end Snapdragons in return.)
And knowing Taiwanese, they simply don't sell companies owners spent their life working on. Very ego driven business culture.
https://www.counterpointresearch.com/mediatek-biggest-smartp...
Didn't Qualcomm beat out a ton of competitors?